Mine can stall without the stall warner being activated - it hasn't got one!
It's not activated by the wing stalling so stall warner is a slight misnomer. It activates when the wing reaches a preset angle of attack. As AoA increases the point at which the airflow divides moves down the leading edge. Once this point goes below the vane it is lifted by the upward airflow and the warning sounds. It's usually adjustable and set to go off prior to the stall so you have enough time to react and do something before the stall actually occurs. Providing the thing is in good working order and not iced up it should consistently go off at the same AoA, which if it is in adjustment should be below the stalling AoA.
However if you were to suddenly pull a lot of G at low speed you could easily leave yourself no time to react.
(Above refers to the vane type, haven't thought about the suction version.)